Construction of abelian varieties with given monodromy (Q2571736)

This paper studies certain algebraic subgroups of a unitary group that is compact at all archimedean places. The author proves that such algebraic groups occur as monodromy groups of some families of abelian varieties of characteristic \(p \neq 0\). These families are constructed by deforming a \(\mathbb F_p^{\text{ac}}\)-valued point on a Shimura variety of PEL-type associated to the corresponding unitary group, where \(\mathbb F_p^{\text{ac}}\) denotes the algebraic closure of the prime field \(\mathbb F_p\).